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A131355 Partial sums of A065423 plus one. 2
1, 1, 1, 3, 4, 8, 10, 16, 19, 27, 31, 41, 46, 58, 64, 78, 85, 101, 109, 127, 136, 156, 166, 188, 199, 223, 235, 261, 274, 302, 316, 346, 361, 393, 409, 443, 460, 496, 514, 552, 571, 611, 631, 673, 694, 738, 760, 806, 829, 877, 901, 951, 976, 1028, 1054, 1108 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..55.

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

FORMULA

From R. J. Mathar, Jul 17 2009: (Start)

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

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5), n>5. (End)

a(n) = (6*n^2-10*n+17-(1+2n)*(-1)^n)/16. - Wesley Ivan Hurt, Jul 28 2015

MAPLE

A065423 := proc(n) if n mod 2 <> 0 then n-1 ; else n/2-1 ; fi ; end: A131355 := proc(n) 1+add(A065423(i), i=1..n) ; end: seq(A131355(n), n=0..80) ; # R. J. Mathar, Oct 04 2007

MATHEMATICA

Table[(6 n^2 - 10 n + 17 - (1 + 2 n) (-1)^n)/16, {n, 0, 100}] (* Wesley Ivan Hurt, Jul 28 2015 *)

LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 1, 3, 4}, 70] (* Vincenzo Librandi, Jul 29 2015 *)

PROG

(Magma) [(6*n^2-10*n+17-(1+2*n)*(-1)^n)/16: n in [0..70]]; // Vincenzo Librandi, Jul 29 2015

CROSSREFS

Cf. A065423.

Sequence in context: A026494 A043306 A308844 * A092534 A005232 A165272

Adjacent sequences: A131352 A131353 A131354 * A131356 A131357 A131358

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Sep 30 2007

EXTENSIONS

More terms from R. J. Mathar, Oct 04 2007

STATUS

approved

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Last modified December 1 21:09 EST 2022. Contains 358484 sequences. (Running on oeis4.)