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Search: id:A130424
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| A130424 |
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Main diagonal of array A[k,n] = n-th sum of k consecutive k-gonal numbers, k>2. |
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+0
1
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| 4, 30, 125, 365, 854, 1724, 3135, 5275, 8360, 12634, 18369, 25865, 35450, 47480, 62339, 80439, 102220, 128150, 158725, 194469, 235934, 283700, 338375, 400595, 471024, 550354, 639305, 738625, 849090, 971504, 1106699, 1255535, 1418900
(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 4 consecutive squares = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = A027575(n). The third row of the array is the sum of 5 consecutive pentagonal numbers.
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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) + ... P(k+2,n+k-1) 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.|..14..30..54...86..126..174..230..294.366.446...=A027575(n).
5.|..40..75.125..190..270..365..475..600.740...
6.|..95.161.251..365..503..665..851.1061.1295...
7.|.196.308.455..637..854.1106.1393.1715.2072...
8.|.364.540.764.1036.1356.1724.2140.2604.3116...
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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+k-1) ; end: A130424 := proc(n) A(n+3, n) ; end: seq(A130424(n), n=0..40) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2007
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CROSSREFS
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Cf. A000217, A000290, A000326, A000384, A000566, A000567, A005448, A005918, A016825, A017377, A129803, A129863, A130423.
Adjacent sequences: A130421 A130422 A130423 this_sequence A130425 A130426 A130427
Sequence in context: A027297 A027445 A027789 this_sequence A005715 A123351 A119697
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 26 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 28 2007
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