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

0,2

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).

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

Prog

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

Crossrefs

Cf. A298033.

Sequence in context: A265676 A054690 A259486 * A054691 A139828 A247905

Adjacent sequences: A298031 A298032 A298033 * A298035 A298036 A298037

Keyword

nonn,easy

Author

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

Status

approved