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A131065 Triangle read by rows: T(n,k)=6*binomial(n,k)-5 (0<=k<=n). 11
1, 1, 1, 1, 7, 1, 1, 13, 13, 1, 1, 19, 31, 19, 1, 1, 25, 55, 55, 25, 1, 1, 31, 85, 115, 85, 31, 1, 1, 37, 121, 205, 205, 121, 37, 1, 1, 43, 163, 331, 415, 331, 163, 43, 1, 1, 49, 211, 499, 751, 751, 499, 211, 49, 1, 1, 55, 265, 715, 1255, 1507, 1255, 715, 265, 55, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums = A131066.

The matrix inverse starts:

1;

-1,1;

6,-7,1;

-66,78,-13,1;

1086,-1284,216,-19,1;

-23826,28170,-4740,420,-25,1;

653406,-772536,129990,-11520,690,-31,1; - R. J. Mathar, Mar 12 2013

LINKS

Indranil Ghosh, Rows 0..120 of triangle, flattened

FORMULA

G.f.=G(t,z)=(1-z-tz+6tz^2)/[(1-z)(1-tz)(1-z-tz)]. - Emeric Deutsch, Jun 20 2007

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

1, 7, 1;

1, 13, 13, 1;

1, 19, 31, 19, 1;

1, 25, 55, 55, 25, 1;

...

MAPLE

T := proc (n, k) if k <= n then 6*binomial(n, k)-5 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # Emeric Deutsch, Jun 20 2007

MATHEMATICA

Table[6*Binomial[n, k]-5, {n, 0, 15}, {k, 0, n}]//Flatten (* Harvey P. Dale, May 15 2016 *)

CROSSREFS

Cf. A109128, A131060 - A131066.

Sequence in context: A217510 A273506 A287326 * A081580 A082110 A275526

Adjacent sequences:  A131062 A131063 A131064 * A131066 A131067 A131068

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 13 2007

EXTENSIONS

More terms from Emeric Deutsch, Jun 20 2007

STATUS

approved

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Last modified February 23 16:15 EST 2020. Contains 332174 sequences. (Running on oeis4.)