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Search: id:A130423
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| A130423 |
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Main diagonal of array A[k,n] = n-th sum of 3 consecutive k-gonal numbers, k>2. |
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+0
2
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| 4, 14, 39, 88, 170, 294, 469, 704, 1008, 1390, 1859, 2424, 3094, 3878, 4785, 5824, 7004, 8334, 9823, 11480, 13314, 15334, 17549, 19968, 22600, 25454, 28539, 31864, 35438, 39270, 43369, 47744, 52404, 57358, 62615, 68184, 74074, 80294, 86853
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The first row of the array is the sum of 3 consecutive triangular numbers = A000217(n) + A000217(n+1) + A000217(n+2) = Centered triangular numbers: 3*n*(n-1)/2 + 1, for n>1. The second row of the array is the sum of 3 consecutive squares = Number of points on surface of square pyramid: 3*n^2 + 2 (n>1). The first column of the array is k+1 = 4, 5, 6, 7, 8, 9, ... The second column of the array is A016825 = 4*n + 2 (for n>2). The third column of the array is A017377 = 10*n + 9 (for n>0).
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LINKS
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Eric Weisstein's World of Mathematics, Polygonal Number
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FORMULA
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a(n) = A[n+2,n] = P(k+2,n) + P(k+2,n+1) + P(k+2,n+2) where P(k,n) = k*((n-2)*k - (n-4))/2.
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EXAMPLE
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The array begins:
k / A[k,n]
3.|.4.10.19.31..46..64..85.109.136.166....=A005448(n+1).
4.|.5.14.29..50..77.110.149.194.245.302...=A005918(n).
5.|.6.18.39..69.108.156.213.279.354.438...=A129863(n).
6.|.7.22.49..88.139.202.277.364.463.574...
7.|.8.26.59.107.170.248.341.449.572.710...
8.|.9.30.69.126.201.294.405.534.681.846...
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MAPLE
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P := proc(k, n) n*((k-2)*n-k+4)/2 ; end: A := proc(k, n) add( P(k, i), i=n..n+2) ; end: A130423 := proc(n) A(n+3, n) ; end: seq(A130423(n), n=0..40) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2007
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CROSSREFS
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Cf. A000217, A000290, A000326, A000384, A000566, A000567, A005448, A005918, A016825, A017377, A129803, A129863.
Adjacent sequences: A130420 A130421 A130422 this_sequence A130424 A130425 A130426
Sequence in context: A124615 A114845 A064463 this_sequence A055484 A055279 A074083
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 26 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2007
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