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A112626 Array, a(n,k) = Sum[C(n,k+m)2^(n-k-m),{m,0,n}], read by rows. 7
1, 3, 1, 9, 5, 1, 27, 19, 7, 1, 81, 65, 33, 9, 1, 243, 211, 131, 51, 11, 1, 729, 665, 473, 233, 73, 13, 1, 2187, 2059, 1611, 939, 379, 99, 15, 1, 6561, 6305, 5281, 3489, 1697, 577, 129, 17, 1, 19683, 19171, 16867, 12259, 6883, 2851, 835, 163, 19, 1, 59049, 58025 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Column 0 is the row sums of A038207 starting at column 0, column 1 is the row sums of A038207 starting at column 1 etc. etc. Helpful suggestions related to Riordan arrays given by Paul Barry.

Riordan array ( 1/(1 - 3*x), x/(1 - 2*x) ). Matrix inverse is a signed version of A209149. - Peter Bala, Jul 17 2013

LINKS

Table of n, a(n) for n=0..56.

FORMULA

a(n, k) = Sum[C(n, k+m)2^(n-k-m), {m, 0, n}].

O.g.f. (by columns): x^k / (1-3x)(1-2x)^k. - Frank Ruskey and class

a(n,k) = Sum[C(n,m)2^(n-m),{m,k,n}]. - Ross La Haye, May 02 2006

Binomial transform (by columns) of A055248.

EXAMPLE

{1};

{3,1};

{9,5,1};

{27,19,7,1};

{81,65,33,9,1};

{243,211,131,51,11,1};

{729,665,473,233,73,13,1}

MATHEMATICA

Flatten[Table[Sum[Binomial[n, k+m]*2^(n-k-m), {m, 0, n}], {n, 0, 10}, {k, 0, n}]]

CROSSREFS

Row sums = n*3^(n-1) + 3^n = A006234(n+3) (Frank Ruskey and class); a(n, 0) = A000244(n); a(n, 1) = A001047(n); a(n, 2) = A066810(n); A038207. A209149 (unsigned matrix inverse).

Sequence in context: A091579 A136159 A005533 * A050155 A270236 A140714

Adjacent sequences:  A112623 A112624 A112625 * A112627 A112628 A112629

KEYWORD

nonn,tabl

AUTHOR

Ross La Haye, Dec 26 2005

EXTENSIONS

More terms from Ross La Haye, Dec 31 2006

STATUS

approved

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Last modified November 12 22:10 EST 2019. Contains 329079 sequences. (Running on oeis4.)