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A153520 Triangular sequence recursion : A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 7*A(n - 2, k - 1). 0
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; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{2, 14, 98, 686, 2058, 8918, 32242, 126910, 479514, 1847398,...}

LINKS

Table of n, a(n) for n=0..50.

FORMULA

A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + 7*A(n - 2, k - 1).

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}

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}] ;

CROSSREFS

Sequence in context: A251809 A016639 A138341 * A153649 A020770 A177003

Adjacent sequences:  A153517 A153518 A153519 * A153521 A153522 A153523

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 28 2008

STATUS

approved

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Last modified October 15 03:09 EDT 2019. Contains 328025 sequences. (Running on oeis4.)