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A261343 50-gonal numbers: a(n) = 48*n*(n-1)/2 + n. 1
0, 1, 50, 147, 292, 485, 726, 1015, 1352, 1737, 2170, 2651, 3180, 3757, 4382, 5055, 5776, 6545, 7362, 8227, 9140, 10101, 11110, 12167, 13272, 14425, 15626, 16875, 18172, 19517, 20910, 22351, 23840, 25377, 26962, 28595, 30276, 32005, 33782, 35607, 37480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 50).

96*a(n) + 23^2 is a square.

LINKS

Table of n, a(n) for n=0..40.

Index to sequences related to polygonal numbers

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = n*(24*n - 23).

G.f.: x*(1+47*x)/(1-x)^3. - Vincenzo Librandi, Aug 17 2015

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Aug 17 2015

MAPLE

A261343:=n->n*(24*n-23): seq(A261343(n), n=0..40); # Wesley Ivan Hurt, Aug 20 2015

PROG

(JavaScript) function a(n){return 48*n*(n-1)/2+n}

(PARI) first(m)=vector(m, n, n--; n*(24*n-23)) \\ Anders Hellström, Aug 15 2015

(MAGMA) [n*(24*n-23): n in [0..40]]; // Vincenzo Librandi, Aug 17 2015

CROSSREFS

Cf. A001107, A051872, A254474.

Sequence in context: A235942 A093300 A283392 * A104152 A044382 A044763

Adjacent sequences:  A261340 A261341 A261342 * A261344 A261345 A261346

KEYWORD

nonn,easy

AUTHOR

Sergey Pavlov, Aug 15 2015

STATUS

approved

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Last modified March 27 06:59 EDT 2017. Contains 284144 sequences.