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A173118 A symmetrical triangle in polynomials of q: q=2;t(n,m,q)=If[m == 0 || m == n, 1, Binomial[n, m] + q*Binomial[n - 2, m - 1] + q^2*If[n - 4 > 0, Binomial[n - 4, m - 2], 0] + q^3*If[n - 6 > 0, Binomial[n - 6, m - 3], 0] + q^4*If[ n - 8 > 0, Binomial[n - 8, m - 4], 0] + q^5*If[n - 10 > 0, Binomial[n - 10, m - 5], 0]] 0
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 10, 6, 1, 1, 7, 20, 20, 7, 1, 1, 8, 27, 40, 27, 8, 1, 1, 9, 35, 75, 75, 35, 9, 1, 1, 10, 44, 110, 150, 110, 44, 10, 1, 1, 11, 54, 154, 276, 276, 154, 54, 11, 1, 1, 12, 65, 208, 430, 552, 430, 208, 65, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 6, 12, 24, 56, 112, 240, 480, 992, 1984,...}.

LINKS

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

FORMULA

q=2;

t(n,m,q)=If[m == 0 || m == n, 1, Binomial[n, m] +

q*Binomial[n - 2, m - 1] +

q^2*If[n - 4 > 0, Binomial[n - 4, m - 2], 0] +

q^3*If[n - 6 > 0, Binomial[n - 6, m - 3], 0] +

q^4*If[ n - 8 > 0, Binomial[n - 8, m - 4], 0] +

q^5*If[n - 10 > 0, Binomial[n - 10, m - 5], 0]]

EXAMPLE

{1},

{1, 1},

{1, 4, 1},

{1, 5, 5, 1},

{1, 6, 10, 6, 1},

{1, 7, 20, 20, 7, 1},

{1, 8, 27, 40, 27, 8, 1},

{1, 9, 35, 75, 75, 35, 9, 1},

{1, 10, 44, 110, 150, 110, 44, 10, 1},

{1, 11, 54, 154, 276, 276, 154, 54, 11, 1},

{1, 12, 65, 208, 430, 552, 430, 208, 65, 12, 1}

MATHEMATICA

Clear[t, n, m, q];

t[n_, m_, q_] := If[m == 0 || m == n, 1, Binomial[n, m] +

q*Binomial[n - 2, m - 1] +

q^2*If[n - 4 > 0, Binomial[n - 4, m - 2], 0] +

q^3*If[n - 6 > 0, Binomial[n - 6, m - 3], 0] +

q^4*If[ n - 8 > 0, Binomial[n - 8, m - 4], 0] +

q^5*If[n - 10 > 0, Binomial[n - 10, m - 5], 0]];

Table[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}], {q, 1, 10}];

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

CROSSREFS

Sequence in context: A099575 A173740 A028275 * A147289 A147566 A204621

Adjacent sequences:  A173115 A173116 A173117 * A173119 A173120 A173121

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 10 2010

STATUS

approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)