A272129 a(n) = 32*n^2 - 56*n + 25.
25, 1, 41, 145, 313, 545, 841, 1201, 1625, 2113, 2665, 3281, 3961, 4705, 5513, 6385, 7321, 8321, 9385, 10513, 11705, 12961, 14281, 15665, 17113, 18625, 20201, 21841, 23545, 25313, 27145, 29041, 31001, 33025, 35113, 37265, 39481, 41761, 44105, 46513, 48985
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014 (page 16).
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[32*n^2 - 56*n + 25: n in [0..50]];
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Maple
[32*n^2-56*n+25$n=0..40]; # Muniru A Asiru, Jan 28 2019
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Mathematica
Table[32 n^2 - 56 n + 25, {n, 0, 40}] LinearRecurrence[{3,-3,1},{25,1,41},50] (* Harvey P. Dale, Jul 03 2018 *) -
PARI
lista(nn) = for(n=0, nn, print1(32*n^2-56*n+25, ", ")); \\ Altug Alkan, Apr 26 2016
Formula
O.g.f.: (25 - 74*x + 113*x^2)/(1-x)^3.
E.g.f.: (25 - 24*x + 32*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
n*a(n) = 1 + 3^5*(n-1)/(n+1) + 5^5*((n-1)*(n-2))/((n+1)*(n+2)) + ... for n >= 1. See A245244. - Peter Bala, Jan 19 2019
Comments