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A063494
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a(n) = (2*n - 1)*(7*n^2 - 7*n + 3)/3.
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19
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1, 17, 75, 203, 429, 781, 1287, 1975, 2873, 4009, 5411, 7107, 9125, 11493, 14239, 17391, 20977, 25025, 29563, 34619, 40221, 46397, 53175, 60583, 68649, 77401, 86867, 97075, 108053, 119829, 132431, 145887, 160225, 175473, 191659, 208811
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OFFSET
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1,2
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COMMENTS
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InterpretA176271as an infinite square array read by antidiagonals, with rows 1,5,11,19,...; 3,9,17,27,... and so on. The sum of the terms in the n X n upper submatrix are s(n) = 1, 18, 93, 296,... = n^2*(7*n^2-1)/6, and a(n) = s(n) - s(n-1) are the first differences. -J. M. Bergot,Jun 27 2013
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LINKS
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FORMULA
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G.f.: x*(1+x)*(1+12*x+x^2)/(1-x)^4. -Colin Barker,Mar 02 2012
E.g.f.: (-3 + 6*x + 21*x^2 + 14*x^3)*exp(x)/3 + 1. -G. C. Greubel,Dec 01 2017
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MATHEMATICA
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Table[(2*n - 1)*(7*n^2 - 7*n + 3)/3, {n, 1, 30}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 17, 75, 203}, 30] (*G. C. Greubel,Dec 01 2017 *)
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PROG
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(PARI) { for (n=1, 1000, write( "b063494.txt", n, "", (2*n - 1)*(7*n^2 - 7*n + 3)/3) ) } \\Harry J. Smith,Aug 23 2009
(Magma) [(2*n - 1)*(7*n^2 - 7*n + 3)/3: n in [1..30]]; //G. C. Greubel,Dec 01 2017
(PARI) x='x+O('x^30); Vec(serlaplace((-3+6*x+21*x^2+14*x^3)*exp(x)/3 + 1)) \\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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