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A298375 Partial sums of A230584. 1
2, 5, 11, 18, 29, 43, 61, 84, 111, 145, 183, 230, 281, 343, 409, 488, 571, 669, 771, 890, 1013, 1155, 1301, 1468, 1639, 1833, 2031, 2254, 2481, 2735, 2993, 3280, 3571, 3893, 4219, 4578, 4941, 5339, 5741, 6180, 6623, 7105, 7591, 8118, 8649, 9223, 9801, 10424 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

FORMULA

Let g = n + ((n + 1) mod 2), then for n > 1,

a(n) = (g^3 + 6*g^2 + 11*g + 18) / 12 - If(n mod 2 = 1, 0, ((n + 2) / 2)^2 + 2).

From Colin Barker, Jan 18 2018: (Start)

G.f.: x*(2 + x - x^2 - x^3 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)^2).

a(n) = (n^3 + 6*n^2 + 14*n) / 12 for n>1 and even.

a(n) = (n^3 + 6*n^2 + 11*n + 18) / 12 for n>1 and odd.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>6.

(End)

EXAMPLE

For n = 5 then a(5) = 2+3+6+7+11 = 29.

MATHEMATICA

CoefficientList[ Series[(2 + x - x^2 - x^3 + 2x^5 - x^6)/((x -1)^4 (x + 1)^2), {x, 0, 50}], x] (* Robert G. Wilson v, Jan 18 2018 *)

PROG

(PARI) Vec(x*(2 + x - x^2 - x^3 + 2*x^5 - x^6) / ((1 - x)^4*(1 + x)^2) + O(x^50)) \\ Colin Barker, Jan 18 2018

CROSSREFS

Cf. A230584.

Sequence in context: A171769 A025200 A264724 * A260037 A132455 A132459

Adjacent sequences:  A298372 A298373 A298374 * A298376 A298377 A298378

KEYWORD

nonn,easy

AUTHOR

Gerald Hillier, Jan 18 2018

STATUS

approved

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Last modified September 21 04:58 EDT 2020. Contains 337267 sequences. (Running on oeis4.)