OFFSET
0,1
COMMENTS
More generally, the ordinary generating function for the sequences of the form k*(n + 1)*(n - 1 + k)/2 is (k*(k - 1)/2 + (k*(3 - k)/2)*x)/(1 - x)^3(see links section).
LINKS
Ilya Gutkovskiy, Sequences of the form k*(n + 1)*(n - 1 + k)/2
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
EXAMPLE
a(0) = 0 + 1 + 2 + 3 + 4 = 10;
a(1) = 0 + 1 + 2 + 3 + 4 + 1 + 2 + 3 + 4 + 5 = 25;
a(2) = 0 + 1 + 2 + 3 + 4 + 1 + 2 + 3 + 4 + 5 + 2 + 3 + 4 + 5 + 6 = 45, etc.
MATHEMATICA
Table[5 (n + 1) ((n + 4)/2), {n, 0, 45}]
Table[Sum[5 (k + 2), {k, 0, n}], {n, 0, 45}]
LinearRecurrence[{3, -3, 1}, {10, 25, 45}, 46]
PROG
(Magma) [5*(n+1)*(n+4)/2: n in [0..50]]; // Vincenzo Librandi, Feb 28 2016
(PARI) a(n) = 5*(n + 1)*(n + 4)/2; \\ Michel Marcus, Feb 29 2016
(PARI) Vec(5*(2-x)/(1-x)^3 + O(x^100)) \\ Altug Alkan, Mar 04 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Feb 27 2016
STATUS
approved