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A176641 A q-form method for the symmetrical triangle sequence was found based on A000384 hexagonal numbers: q=4;c(n,q)=Product[(q*(2*q - 1))^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, 28, 1, 1, 784, 784, 1, 1, 21952, 614656, 21952, 1, 1, 614656, 481890304, 481890304, 614656, 1, 1, 17210368, 377801998336, 10578455953408, 377801998336, 17210368, 1, 1, 481890304, 296196766695424, 232218265089212416 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

q=2 is A158116.

Row sums are:

{1, 2, 30, 1570, 658562, 965009922, 11334094370818, 465028924675596290,

152930125093708892962818, 175688857026481498894387773442,

1617764592252975012649795108084383746,...}.

LINKS

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

FORMULA

q=4;

c(n,q)=Product[(q*(2*q - 1))^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, 28, 1},

{1, 784, 784, 1},

{1, 21952, 614656, 21952, 1},

{1, 614656, 481890304, 481890304, 614656, 1},

{1, 17210368, 377801998336, 10578455953408, 377801998336, 17210368, 1},

{1, 481890304, 296196766695424, 232218265089212416, 232218265089212416, 296196766695424, 481890304, 1},

{1, 13492928512, 232218265089212416, 5097655355238390956032, 142734349946674946768896, 5097655355238390956032, 232218265089212416, 13492928512, 1},

{1, 377801998336, 182059119829942534144, 111903730358193158266814464, 87732524600823436081182539776, 87732524600823436081182539776, 111903730358193158266814464, 182059119829942534144, 377801998336, 1},

{1, 10578455953408, 142734349946674946768896, 2456510688823056210273111113728, 53925322641043729927915335168557056, 1509909033949224437981629384719597568, 53925322641043729927915335168557056, 2456510688823056210273111113728, 142734349946674946768896, 10578455953408, 1}

MATHEMATICA

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

c[n_, q_] = Product[(q*(2*q - 1))^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. A000384, A158116

Sequence in context: A040785 A040784 A174188 * A040796 A040797 A187595

Adjacent sequences:  A176638 A176639 A176640 * A176642 A176643 A176644

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 22 2010

STATUS

approved

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Last modified August 18 07:11 EDT 2019. Contains 326072 sequences. (Running on oeis4.)