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A126274 Partial sum of hexagonal prism numbers (A005915). 5
1, 15, 72, 220, 525, 1071, 1960, 3312, 5265, 7975, 11616, 16380, 22477, 30135, 39600, 51136, 65025, 81567, 101080, 123900, 150381, 180895, 215832, 255600, 300625, 351351, 408240, 471772, 542445, 620775, 707296, 802560, 907137, 1021615 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This is a 4-dimensional pyramidal number sequence whose slices are hexagonal prism numbers. Hexagonal prism numbers (A005915): (n + 1)*(3*n^2 + 3*n + 1).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = sum( i=0..n, (i + 1)*(3*i^2 + 3*i + 1) ) = (3*n^4 + 6*n^3 + 3*n^2)/4 + 2*n^3 + 5*n^2 + 4*n + 1.

a(n) = (1/4)*(n + 1)^2*(n + 2)*(3*n + 2). - N-E. Fahssi, May 03 2008

G.f.: (1 + 10 x + 7 x^2)/(1 - x)^5. - N-E. Fahssi, May 03 2008

a(n) = (n+1)*A000578(n+1) - sum( i=0..n, A000578(i) ). [Bruno Berselli, Apr 24 2010]

a(n) = sum_{i=1..n} sum_{j=1..n} sum_{k=1..n} max(i,j,k). - Enrique Pérez Herrero, Feb 26 2013

a(n) = A000217(n+1)*A000326(n+1). [Bruno Berselli, Dec 13 2013]

EXAMPLE

a(16) = 1 + 14 + 57 + 148 + 305 + 546 + 889 + 1352 + 1953 + 2710 + 3641 + 4764 + 6097 + 7658 + 9465 + 11536 + 13889 = 65025 = 3^2 * 5^2 * 17^2.

PROG

(MAGMA) [1/4*(n + 1)^2*(n + 2)*(3*n + 2): n in [0..30]]; // Vincenzo Librandi, May 16 2011

CROSSREFS

Cf. A000217, A000326, A000578, A005915.

Sequence in context: A253476 A145053 A168298 * A241234 A212097 A212098

Adjacent sequences:  A126271 A126272 A126273 * A126275 A126276 A126277

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Mar 09 2007

EXTENSIONS

Corrected and extended by Vincenzo Librandi, May 16 2011

STATUS

approved

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Last modified December 6 06:58 EST 2016. Contains 278775 sequences.