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A194801
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Square array read by antidiagonals: T(n,k) = k*((n+1)*k-n+1)/2, k = 0, +- 1, +- 2,..., n >= 0.
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3
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0, 0, 1, 0, 1, 0, 0, 1, 1, 3, 0, 1, 2, 4, 1, 0, 1, 3, 5, 4, 6, 0, 1, 4, 6, 7, 9, 3, 0, 1, 5, 7, 10, 12, 9, 10, 0, 1, 6, 8, 13, 15, 15, 16, 6, 0, 1, 7, 9, 16, 18, 21, 22, 16, 15, 0, 1, 8, 10, 19, 21, 27, 28, 26, 25, 10, 0, 1, 9, 11, 22, 24, 33, 34, 36, 35
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OFFSET
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0,10
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COMMENTS
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Note that a single formula gives several types of numbers. Row 0 lists 0 together the Molien series for 3-dimensional group [2,k]+ = 22k. Row 1 lists, except first zero, the squares repeated. If n >= 2, row n lists the generalized (n+3)-gonal numbers, for example: row 2 lists the generalized pentagonal numbers A001318. See some other examples in the cross-references section.
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LINKS
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EXAMPLE
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Array begins:
(A008795): 0, 1, 0, 3, 1, 6, 3, 10, 6, 15, 10...
(A008794): 0, 1, 1, 4, 4, 9, 9, 16, 16, 25, 25...
A001318: 0, 1, 2, 5, 7, 12, 15, 22, 26, 35, 40...
A000217: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55...
A085787: 0, 1, 4, 7, 13, 18, 27, 34, 46, 55, 70...
A001082: 0, 1, 5, 8, 16, 21, 33, 40, 56, 65, 85...
A118277: 0, 1, 6, 9, 19, 24, 39, 46, 66, 75, 100...
A074377: 0, 1, 7, 10, 22, 27, 45, 52, 76, 85, 115...
A195160: 0, 1, 8, 11, 25, 30, 51, 58, 86, 95, 130...
A195162: 0, 1, 9, 12, 28, 33, 57, 64, 96, 105, 145...
A195313: 0, 1, 10, 13, 31, 36, 63, 70, 106, 115, 160...
A195818: 0, 1, 11, 14, 34, 39, 69, 76, 116, 125, 175...
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PROG
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(GW-BASIC)
200 DIM T(11, 10)
210 FOR N=0 TO 11
220 FOR J=0 TO 5
230 IF J>0 THEN T(N, K)= J *((N+1)* J -N+1)/2: K=K+1
240 T(N, K)=(-J)*((N+1)*(-J)-N+1)/2: K=K+1
250 NEXT J
260 K=0
270 NEXT N
299 '...
300 'PRINT SQUARE ARRAY T(N, K) (see example)
310 FOR N=0 TO 11
320 FOR K=0 TO 10
330 PRINT T(N, K);
340 NEXT K
350 PRINT
360 NEXT N
500 END
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CROSSREFS
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Rows (0-11): 0 together with A008795, (truncated A008794), A001318, A000217, A085787, A001082, A118277, A074377, A195160, A195162, A195313, A195818
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KEYWORD
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AUTHOR
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STATUS
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approved
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