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A153520
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Triangular sequence recursion : A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 7*A(n - 2, k - 1).
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0
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2, 7, 7, 2, 94, 2, 2, 341, 341, 2, 2, 357, 1340, 357, 2, 2, 373, 4084, 4084, 373, 2, 2, 389, 6956, 17548, 6956, 389, 2, 2, 405, 9956, 53092, 53092, 9956, 405, 2, 2, 421, 13084, 111740, 229020, 111740, 13084, 421, 2, 2, 437, 16340, 194516, 712404, 712404
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{2, 14, 98, 686, 2058, 8918, 32242, 126910, 479514, 1847398,...}
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 7*A(n - 2, k - 1).
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EXAMPLE
| {2},
{7, 7},
{2, 94, 2},
{2, 341, 341, 2},
{2, 357, 1340, 357, 2},
{2, 373, 4084, 4084, 373, 2},
{2, 389, 6956, 17548, 6956, 389, 2},
{2, 405, 9956, 53092, 53092, 9956, 405, 2},
{2, 421, 13084, 111740, 229020, 111740, 13084, 421, 2},
{2, 437, 16340, 194516, 712404, 712404, 194516, 16340, 437, 2}
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MATHEMATICA
| Clear[t, n, m, A, a];
j = 4; A[2, 1] := A[2, 2] = Prime[j];
A[3, 2] = 2*Prime[j]^2 - 4;
A[4, 2] = A[4, 3] = Prime[j]^3 - 2;;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + Prime[j]*A[n - 2, k - 1];
Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%] Table[Sum[A[n, m], {m, 1, n}], {n, 1, 10}] ; Table[Sum[A[n, m], {m, 1, n}]/(2*Prime[j]^(n - 1)), {n, 1, 10}] ;
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CROSSREFS
| Sequence in context: A159790 A016639 A138341 * A153649 A020770 A177003
Adjacent sequences: A153517 A153518 A153519 * A153521 A153522 A153523
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 28 2008
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