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A202141
a(n) = 13*n^2 - 16*n + 5.
4
5, 2, 25, 74, 149, 250, 377, 530, 709, 914, 1145, 1402, 1685, 1994, 2329, 2690, 3077, 3490, 3929, 4394, 4885, 5402, 5945, 6514, 7109, 7730, 8377, 9050, 9749, 10474, 11225, 12002, 12805, 13634, 14489, 15370, 16277, 17210, 18169, 19154, 20165, 21202, 22265
OFFSET
0,1
COMMENTS
Numbers of the form (r*n - r + 1)^2 + ((r+1)*n - r)^2; in this case, r=2.
Inverse binomial transform of this sequence: 5,-3, 26, 0, 0 (0 continued).
FORMULA
G.f.: (5 - 13*x + 34*x^2)/(1-x)^3.
a(n) = A161587(n-1) + 1 with A161587(-1) = 4.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. - Wesley Ivan Hurt, Oct 09 2017
E.g.f.: (5 - 3*x + 13*x^2)*exp(x). - Elmo R. Oliveira, Oct 20 2024
MAPLE
A202141:=n->13*n^2-16*n+5: seq(A202141(n), n=0..100); # Wesley Ivan Hurt, Oct 09 2017
MATHEMATICA
Table[13 n^2 - 16 n + 5, {n, 0, 42}]
PROG
(PARI) for(n=0, 42, print1(13*n^2-16*n+5", "));
(Magma) [13*n^2-16*n+5: n in [0..42]];
CROSSREFS
Cf. A190816 (r=1), A154355 (r=3), A161587.
Sequence in context: A038244 A135138 A128712 * A100080 A117734 A007572
KEYWORD
nonn,easy,changed
AUTHOR
Bruno Berselli, Dec 12 2011
STATUS
approved