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A195047 Concentric 17-gonal numbers. 7
0, 1, 17, 35, 68, 103, 153, 205, 272, 341, 425, 511, 612, 715, 833, 953, 1088, 1225, 1377, 1531, 1700, 1871, 2057, 2245, 2448, 2653, 2873, 3095, 3332, 3571, 3825, 4081, 4352, 4625, 4913, 5203, 5508, 5815, 6137, 6461, 6800, 7141, 7497, 7855, 8228, 8603, 8993 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also concentric heptadecagonal numbers or concentric heptakaidecagonal numbers.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

a(n) = 17*n^2/4+13*((-1)^n-1)/8.

G.f.: -x*(1+15*x+x^2) / ( (1+x)*(x-1)^3 ). a(n)+a(n+1) = A069130(n+1). - R. J. Mathar, Sep 28 2011

a(n) = a(-n) = (34*n^2+13*(-1)^n-13)/8.  a(n) = A151978(A061925(n)). - Bruno Berselli, Sep 29 2011

MATHEMATICA

LinearRecurrence[{2, 0, -2, 1}, {0, 1, 17, 35}, 50] (* Harvey P. Dale, Dec 23 2017 *)

PROG

(PARI) a(n)=17*n^2/4+13*((-1)^n-1)/8 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Column 17 of A195040.

Cf. A032527, A032528, A195046, A195146, A195147, A195048.

Sequence in context: A004921 A239129 A212427 * A198587 A041570 A041572

Adjacent sequences:  A195044 A195045 A195046 * A195048 A195049 A195050

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 27 2011

EXTENSIONS

Typo in formula fixed by Ivan Panchenko, Nov 08 2013

STATUS

approved

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Last modified October 19 09:55 EDT 2018. Contains 316349 sequences. (Running on oeis4.)