OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
EXAMPLE
a(0) = 0 + 1*2 = 2;
a(1) = 0 + 1*2 + 3 + 4*5 = 25;
a(2) = 0 + 1*2 + 3 + 4*5 + 6 + 7*8 = 87;
a(3) = 0 + 1*2 + 3 + 4*5 + 6 + 7*8 + 9 + 10*11 = 206;
a(4) = 0 + 1*2 + 3 + 4*5 + 6 + 7*8 + 9 + 10*11 + 12 + 13*14 = 400, etc.
MATHEMATICA
Table[(n + 1) ((6 n^2 + 15 n + 4)/2), {n, 0, 38}]
Table[Sum[3 k + (3 k + 1) (3 k + 2), {k, 0, n}], {n, 0, 38}]
LinearRecurrence[{4, -6, 4, -1}, {2, 25, 87, 206}, 39]
PROG
(PARI) Vec((2 + 17*x - x^2)/(x - 1)^4 + O(x^50)) \\ Michel Marcus, Feb 22 2016
(Magma) [(n+1)*(6*n^2+15*n+4)/2: n in [0..40]]; // Vincenzo Librandi, Feb 22 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Feb 20 2016
STATUS
approved