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A349682 a(n) = A000292(6*n + 1) where A000292 are the tetrahedral numbers. 1
1, 84, 455, 1330, 2925, 5456, 9139, 14190, 20825, 29260, 39711, 52394, 67525, 85320, 105995, 129766, 156849, 187460, 221815, 260130, 302621, 349504, 400995, 457310, 518665, 585276, 657359, 735130, 818805, 908600, 1004731, 1107414, 1216865, 1333300, 1456935, 1587986 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..35.

Euclid of Alexandria, Elements, VII Def. 17, p. 194, 300 BCE.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 1 + 11*n + 36*n^2 + 36*n^3 = (1 + 2*n)*(1 + 3*n)*(1 + 6*n).

G.f.: (1 + 80*x + 125*x^2 + 10*x^3)/(1 - x)^4. - Stefano Spezia, Nov 29 2021

MATHEMATICA

nterms=50; Table[36n^3+36n^2+11n+1, {n, 0, nterms-1}] (* Paolo Xausa, Nov 25 2021 *)

PROG

(PARI) a(n) = subst(m*(m+1)*(m+2)/6, 'm, 6*n+1); \\ Michel Marcus, Dec 16 2021

(Python)

def A349682(n): return n*(n*(36*n + 36) + 11) + 1 # Chai Wah Wu, Dec 27 2021

CROSSREFS

Cf. A000292, A002492, A016921, A000447.

Sequence in context: A251300 A251293 A251254 * A064198 A329935 A233055

Adjacent sequences:  A349679 A349680 A349681 * A349683 A349684 A349685

KEYWORD

easy,nonn

AUTHOR

Ralf Steiner, Nov 25 2021

STATUS

approved

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)