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A063490
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a(n) = (2*n - 1)*(7*n^2 - 7*n + 6)/6.
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22
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1, 10, 40, 105, 219, 396, 650, 995, 1445, 2014, 2716, 3565, 4575, 5760, 7134, 8711, 10505, 12530, 14800, 17329, 20131, 23220, 26610, 30315, 34349, 38726, 43460, 48565, 54055, 59944, 66246, 72975, 80145, 87770, 95864, 104441, 113515
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OFFSET
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1,2
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COMMENTS
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a(n) is also the sum of terms that are in the n-th finite row and in the n-th finite column of the square [1,n]x[1,n] of the natural number arrayA000027;e.g., the [1,3]x[1,3] square is
1..3..6
2..5..9
4..8..13,
so that a(1) = 1, a(2) = 2 + 3 + 5 = 10, a(3) = 4 + 6 + 8 + 9 + 13 = 40.
Hence the partial sums giveA185505.(End)
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LINKS
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FORMULA
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G.f.: x*(1+x)*(1+5*x+x^2)/(1-x)^4. -Colin Barker,Mar 02 2012
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: (-6 + 12*x + 21*x^2 + 14*x^3)*exp(x)/6 + 1. (End)
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MATHEMATICA
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Table[(2*n-1)*(7*n^2-7*n+6)/6, {n, 1, 50}] (* or *) LinearRecurrenc[{4, -6, 4, -1}, {1, 10, 40, 105}, 50] (*G. C. Greubel,Dec 01 2017 *)
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PROG
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(PARI) { for (n=1, 1000, write( "b063490.txt", n, "", (2*n - 1)*(7*n^2 - 7*n + 6)/6) ) } \\Harry J. Smith,Aug 23 2009
(PARI) x='x+O('x^30); Vec(serlaplace((-6 + 12*x + 21*x^2 + 14*x^3 )*exp(x)/6 + 1)) \\G. C. Greubel,Dec 01 2017
(Magma) [(2*n-1)*(7*n^2-7*n+6)/6: n in [1..30]]; //G. C. Greubel,Dec 01 2017
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CROSSREFS
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1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6,... givesA049480,A005894,A063488,A001845,A063489,A005898,A063490,A057813,A063491,A005902,A063492,A005917,A063493,A063494,A063495,A063496.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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