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A173741 T(n,k) = binomial(n,k) + 4 for 1 <= k <= n - 1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, triangle read by rows. 2
1, 1, 1, 1, 6, 1, 1, 7, 7, 1, 1, 8, 10, 8, 1, 1, 9, 14, 14, 9, 1, 1, 10, 19, 24, 19, 10, 1, 1, 11, 25, 39, 39, 25, 11, 1, 1, 12, 32, 60, 74, 60, 32, 12, 1, 1, 13, 40, 88, 130, 130, 88, 40, 13, 1, 1, 14, 49, 124, 214, 256, 214, 124, 49, 14, 1, 1, 15, 59, 169, 334, 466, 466, 334, 169, 59, 15, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

For n >= 1, row n sums to 2*A100314(n).

LINKS

Table of n, a(n) for n=0..77.

FORMULA

From Franck Maminirina Ramaharo, Dec 09 2018:(Start)

T(n,k) = A007318(n,k) + 2*(1 - A103451(n,k)).

T(n,k) = 5*A007318(n,k) - 4*A132044(n,k).

n-th row polynomial is 2*(1 - (-1)^(2^n)) + (1 + x)^n + 4*(x - x^n)/(1 - x).

G.f.: (1 - (1 + x)*y + 5*x*y^2 - 4*(x + x^2)*y^3)/((1 - y)*(1 - x*y)*(1 - y - x*y)).

E.g.f.: (4 - 4*x + 4*x*exp(y) - 4*exp(x*y) + (1 - x)*exp((1 + x)*y))/(1 - x). (End)

EXAMPLE

Triangle begins:

  1;

  1,  1;

  1,  6,  1;

  1,  7,  7,   1;

  1,  8, 10,   8,   1;

  1,  9, 14,  14,   9,   1;

  1, 10, 19,  24,  19,  10,   1;

  1, 11, 25,  39,  39,  25,  11,   1;

  1, 12, 32,  60,  74,  60,  32,  12,  1;

  1, 13, 40,  88, 130, 130,  88,  40, 13,  1;

  1, 14, 49, 124, 214, 256, 214, 124, 49, 14, 1;

  ...

MATHEMATICA

T[n_, m_] = Binomial[n, m] + 4*If[m*(n - m) > 0, 1, 0];

Flatten[Table[T[n, m], {n, 0, 10}, {m, 0, n}]]

PROG

(Maxima) T(n, k) := if k = 0 or k = n then 1 else binomial(n, k) + 4$

create_list(T(n, k), n, 0, 12, k, 0, n); /* Franck Maminirina Ramaharo, Dec 09 2018 */

CROSSREFS

Cf. A007318, A103451, A132044, A156050, A173740, A173742.

Sequence in context: A176348 A176264 A195397 * A171147 A171695 A179233

Adjacent sequences:  A173738 A173739 A173740 * A173742 A173743 A173744

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 23 2010

EXTENSIONS

Edited and name clarified by Franck Maminirina Ramaharo, Dec 09 2018

STATUS

approved

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Last modified September 20 13:59 EDT 2019. Contains 327238 sequences. (Running on oeis4.)