A279895 a(n) = n*(5*n + 11)/2.
0, 8, 21, 39, 62, 90, 123, 161, 204, 252, 305, 363, 426, 494, 567, 645, 728, 816, 909, 1007, 1110, 1218, 1331, 1449, 1572, 1700, 1833, 1971, 2114, 2262, 2415, 2573, 2736, 2904, 3077, 3255, 3438, 3626, 3819, 4017, 4220, 4428, 4641, 4859, 5082, 5310, 5543, 5781, 6024, 6272, 6525
Offset: 0
Links
- Bruno Berselli, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[n*(5*n+11)/2: n in [0..60]];
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Mathematica
Table[n (5 n + 11)/2, {n, 0, 60}] LinearRecurrence[{3,-3,1},{0,8,21},60] (* Harvey P. Dale, Nov 14 2022 *) -
PARI
vector(60, n, n--; n*(5*n+11)/2)
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Python
[n*(5*n+11)/2 for n in range(60)]
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Sage
[n*(5*n+11)/2 for n in range(60)]
Formula
O.g.f.: x*(8 - 3*x)/(1 - x)^3.
E.g.f.: x*(16 + 5*x)*exp(x)/2.
a(n+h) - a(n-h) = h*A017281(n+1), with h>=0. A particular case:
a(n) - a(-n) = 11*n = A008593(n).
a(n+h) + a(n-h) = 2*a(n) + A033429(h), with h>=0. A particular case:
a(n) + a(-n) = A033429(n).
a(n) - a(n-2) = A017281(n) for n>1. Also:
40*a(n) + 121 = A017281(n+1)^2.
Comments