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Search: id:A137227
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| A137227 |
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A triangular sequence of queues like A122525 that depends on a Fibonacci sequence in a differential way by replacing: m->A000045[m+1]-A000045[m]. |
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+0
1
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| 1, 1, 1, 2, 2, 2, 6, 9, 9, 22, 24, 64, 64, 266, 708, 120, 625, 625, 4536, 17457, 108129, 720, 7776, 7776, 100392, 563088, 5709120, 52517688, 5040, 117649, 117649, 2739472, 22516209, 375217945, 5489293264, 92757410569, 40320, 2097152
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The value of this type of sequence is two fold:
1) it allows a sequence based differential generalization
2) the rate of change/ curve slope can be controlled and changed
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FORMULA
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f(n) = A000045[m+1]-A000045[m] t(n,m)=If[m == 0, n!, (f[m]^n*n^(n - 1) - Sum[n^i*f[m]^i/i!, {i, 0, n - 1}]*(f[m] - 1)*Gamma[n])];
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EXAMPLE
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{1},
{1, 1},
{2, 2, 2},
{6, 9, 9, 22},
{24, 64, 64, 266, 708},
{120, 625, 625, 4536, 17457, 108129},
{720, 7776, 7776, 100392, 563088, 5709120, 52517688},
{5040, 117649, 117649, 2739472, 22516209, 375217945, 5489293264, 92757410569},
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MATHEMATICA
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Clear [a, t] a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2]; f[n_] := a[n + 1] - a[n]; t[n_, m_] := If[m == 0, n!, (f[m]^n*n^(n - 1) - Sum[n^i*f[m]^ i/i!, {i, 0, n - 1}]*(f[m] - 1)*Gamma[n])]; a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Cf. A000045, A122525.
Adjacent sequences: A137224 A137225 A137226 this_sequence A137228 A137229 A137230
Sequence in context: A105341 A121698 A087482 this_sequence A052537 A024945 A032306
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 07 2008
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