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A176631 A q-form method for the symmetrical triangle sequence was found based on A000326 pentagonal numbers: q=4;c(n,q)=Product[(q*(3*q - 1)/2)^i, {i, 1, n}];t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)- c(n,q)/(c(0,q)*c(n-0,q)+1 0
1, 1, 1, 1, 22, 1, 1, 484, 484, 1, 1, 10648, 234256, 10648, 1, 1, 234256, 113379904, 113379904, 234256, 1, 1, 5153632, 54875873536, 1207269217792, 54875873536, 5153632, 1, 1, 113379904, 26559922791424, 12855002631049216 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 24, 970, 255554, 227228322, 1317031272130, 25763125334441090,

3285147342380140061442, 1413774007744906960081994242,

3966057262366739303492486159576066,...}.

Integer sum:

Sum[3*n - 2, {n, 1, q}]=q*(3*q-1)/2

LINKS

Table of n, a(n) for n=0..31.

FORMULA

q=4;

c(n,q)=Product[(q*(3*q - 1)/2)^i, {i, 1, n}];

t(n,m,q)=c(n,q)/(c(m,q)*c(n-m,q)- c(n,q)/(c(0,q)*c(n-0,q)+1

EXAMPLE

{1},

{1, 1},

{1, 22, 1},

{1, 484, 484, 1},

{1, 10648, 234256, 10648, 1},

{1, 234256, 113379904, 113379904, 234256, 1},

{1, 5153632, 54875873536, 1207269217792, 54875873536, 5153632, 1},

{1, 113379904, 26559922791424, 12855002631049216, 12855002631049216, 26559922791424, 113379904, 1},

{1, 2494357888, 12855002631049216, 136880068015412051968, 3011361496339065143296, 136880068015412051968, 12855002631049216, 2494357888, 1},

{1, 54875873536, 6221821273427820544, 1457498964228107529355264, 705429498686404044207947776, 705429498686404044207947776, 1457498964228107529355264, 6221821273427820544, 54875873536, 1},

{1, 1207269217792, 3011361496339065143296, 15519448971100888972574851072, 165251092644282265779977014214656, 3635524038174209847159494312722432, 165251092644282265779977014214656, 15519448971100888972574851072, 3011361496339065143296, 1207269217792, 1}

MATHEMATICA

Clear[t, n, m, c, q];

c[n_, q_] = Product[(q*(3*q - 1)/2)^i, {i, 1, n}];

t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - c[n, q]/(c[0, q]*c[n - 0, q]) + 1;

Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]

CROSSREFS

Cf. A000326, A118190

Sequence in context: A291074 A225076 A022185 * A015150 A040493 A040494

Adjacent sequences:  A176628 A176629 A176630 * A176632 A176633 A176634

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 22 2010

STATUS

approved

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Last modified April 20 03:12 EDT 2019. Contains 322294 sequences. (Running on oeis4.)