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A085787 Generalized heptagonal numbers: n*(5*n-3)/2, n=0, +-1, +-2 +-3, ... 45
0, 1, 4, 7, 13, 18, 27, 34, 46, 55, 70, 81, 99, 112, 133, 148, 172, 189, 216, 235, 265, 286, 319, 342, 378, 403, 442, 469, 511, 540, 585, 616, 664, 697, 748, 783, 837, 874, 931, 970, 1030, 1071, 1134, 1177, 1243, 1288, 1357, 1404, 1476, 1525, 1600, 1651, 1729 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Zero together with the partial sums of A080512. - Omar E. Pol, Sep 10 2011

Second heptagonal numbers (A147875) and positive terms of A000566 interleaved. - Omar E. Pol, Aug 04 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index to sequences with linear recurrences with constant coefficients, signature (1,2,-2,-1,1)

FORMULA

a(n) = A000217(n)+A000217(floor(n/2)).

a(2n-1) = A000566(n).

G.f.: x*(1+3*x+x^2)/ ((1-x)*(1-x^2)^2). a(-1-n)=a(n). - Michael Somos, Oct 17 2006

a(n)=5*n*(n+1)/8-1/16+(-1)^n*(2*n+1)/16. - R. J. Mathar, Jun 29 2009

a(n) = (A000217(n) + A001082(n))/2 = (A001318(n) + A118277(n))/2. - Omar E. Pol, Jan 11 2013

a(n) = A002378(n) - A001318(n). - Omar E. Pol, Oct 23 2013

EXAMPLE

a(5)=t(5)+t(2)=15+8=18

MATHEMATICA

Select[Table[(n*(n+1)/2-1)/5, {n, 500}], IntegerQ] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2012 *)

PROG

(PARI) t(n)=n*(n+1)/2 for(i=0, 40, print1(", "t(i)+t(floor(i/2))))

(PARI) {a(n)= (5*(-n\2)^2 -(-n\2)*3*(-1)^n)/2} /* Michael Somos, Oct 17 2006 */

(MAGMA) [5*n*(n+1)/8-1/16+(-1)^n*(2*n+1)/16: n in [0..60]]; // Vincenzo Librandi, Sep 11 2011

CROSSREFS

Cf. A001318 [t(i)-t(floor(i/2))].

Column 3 of A195152.

Generalized k-gonal numbers, k>=5: A001318, A000217, this sequence, A001082, A118277, A074377, A195160, A195162, A195313, A195818.

Sequence in context: A049698 A074136 * A111710 A191138 A075315 A238327

Adjacent sequences:  A085784 A085785 A085786 * A085788 A085789 A085790

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jul 23 2003

EXTENSIONS

New name from T. D. Noe, Apr 21 2006

Formula in sequence name added by Omar E. Pol, May 28 2012

STATUS

approved

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Last modified September 21 08:08 EDT 2014. Contains 247023 sequences.