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Search: id:A146988
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| A146988 |
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Symmetrically shifted Pascal triangle: t(n,m)=If[n < 2, Binomial[n, m], Binomial[n, m] + 4^(n - 1)*Binomial[n - 2, m - 1]]. |
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+0
1
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| 1, 1, 1, 1, 6, 1, 1, 19, 19, 1, 1, 68, 134, 68, 1, 1, 261, 778, 778, 261, 1, 1, 1030, 4111, 6164, 4111, 1030, 1, 1, 4103, 20501, 40995, 40995, 20501, 4103, 1, 1, 16392, 98332, 245816, 327750, 245816, 98332, 16392, 1, 1, 65545, 458788, 1376340, 2293886
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are:{1, 2, 8, 40, 272, 2080, 16448, 131200, 1048832, 8389120, 67109888}.
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FORMULA
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t(n,m)=If[n < 2, Binomial[n, m], Binomial[n, m] + 4^(n - 1)*Binomial[n - 2, m - 1]].
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EXAMPLE
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{1}, {1, 1}, {1, 6, 1}, {1, 19, 19, 1}, {1, 68, 134, 68, 1}, {1, 261, 778, 778, 261, 1}, {1, 1030, 4111, 6164, 4111, 1030, 1}, {1, 4103, 20501, 40995, 40995, 20501, 4103, 1}, {1, 16392, 98332, 245816, 327750, 245816, 98332, 16392, 1}, {1, 65545, 458788, 1376340, 2293886, 2293886, 1376340, 458788, 65545, 1}, {1, 262154, 2097197, 7340152, 14680274, 18350332, 14680274, 7340152, 2097197, 262154, 1}
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MATHEMATICA
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Table[If[n <2, Binomial[n, m], Binomial[n, m] + 4^(n - 1)*Binomial[n - 2, m - 1]], {n, 0, 10}, {m, 0, n}]; Flatten[%]
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CROSSREFS
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A028262
Sequence in context: A157632 A141690 A146957 this_sequence A060972 A144066 A056941
Adjacent sequences: A146985 A146986 A146987 this_sequence A146989 A146990 A146991
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 04 2008
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