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A298034 Partial sums of A298033. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 18 10:35 EDT 2021. Contains 347518 sequences. (Running on oeis4.)