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A131061 Triangle read by rows: T(n,k) = 4*binomial(n,k)-3 (0 <= k <= n). 10
1, 1, 1, 1, 5, 1, 1, 9, 9, 1, 1, 13, 21, 13, 1, 1, 17, 37, 37, 17, 1, 1, 21, 57, 77, 57, 21, 1, 1, 25, 81, 137, 137, 81, 25, 1, 1, 29, 109, 221, 277, 221, 109, 29, 1, 1, 33, 141, 333, 501, 501, 333, 141, 33, 1, 1, 37, 177, 477, 837, 1005, 837, 477, 177, 37, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums = A131062: (1, 2, 7, 20, 49, 110, 235, ...); the binomial transform of (1, 1, 4, 4, 4, ...).

Triangle equals 4*A007318 - 3*A000012 as infinite lower triangular matrices. - Emeric Deutsch, Jun 21 2007

LINKS

Table of n, a(n) for n=0..65.

FORMULA

G.f. = G(t,z) = (1 - z - tz + 4tz^2)/((1-z)(1-tz)(1-z-tz)). - Emeric Deutsch, Jun 21 2007

EXAMPLE

First few rows of the triangle are

  1;

  1,  1;

  1,  5,  1;

  1,  9,  9,  1;

  1, 13, 21, 13,  1;

  1, 17, 37, 37, 17,  1;

  1, 21, 57, 77, 57, 21, 1;

  ...

MAPLE

T := proc (n, k) if k <= n then 4*binomial(n, k)-3 else 0 end if end proc; for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 21 2007

CROSSREFS

Cf. A131060, A131062, A131063, A131064, A131065, A131066.

Sequence in context: A157174 A183450 A296128 * A157169 A081578 A184883

Adjacent sequences:  A131058 A131059 A131060 * A131062 A131063 A131064

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 13 2007

EXTENSIONS

More terms from Emeric Deutsch, Jun 21 2007

STATUS

approved

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Last modified January 19 04:09 EST 2020. Contains 331031 sequences. (Running on oeis4.)