A298034 Partial sums of A298033.

1, 7, 19, 43, 73, 115, 163, 223, 289, 367, 451, 547, 649, 763, 883, 1015, 1153, 1303, 1459, 1627, 1801, 1987, 2179, 2383, 2593, 2815, 3043, 3283, 3529, 3787, 4051, 4327, 4609, 4903, 5203, 5515, 5833, 6163, 6499, 6847, 7201, 7567, 7939, 8323, 8713, 9115, 9523, 9943, 10369, 10807, 11251, 11707

Offset: 0

Author

N. J. A. Sloane, Jan 21 2018, corrected Jan 24 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A298033.

Programs

PARI

Vec((1 + 5*x + 5*x^2 + 7*x^3) / ((1 - x)^3*(1 + x)) + O(x^50)) \\ Colin Barker, Jan 25 2018

Formula

G.f.: (1 + 5*x + 5*x^2 + 7*x^3) / ((1 - x)^3*(1 + x)).

From Colin Barker, Jan 25 2018: (Start)

a(n) = (9*n^2 + 2) / 2 for n even.

a(n) = (9*n^2 + 5) / 2 for n odd.

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>3. (End)

a(4*k+r) = 36*k*(2*k + r) + a(r) for r = 0..3. Example: if n=29 then k=7 and r=1, hence a(29) = 36*7*(2*7 + 1) + 7 = 3787. - Bruno Berselli, Jan 25 2018