login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176795 A symmetrical triangle sequence:q=4;f(n,m,q)=Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];t(n,m,q)=1 - (f(n, k, q) + f(n, 2*n - k, q) - (f(n, 1, q) + f(n, 2*n - 1, q))) 0
1, 1, 1, 1, 37, 1, 1, 361, 361, 1, 1, 3025, 3601, 3025, 1, 1, 24481, 30241, 30241, 24481, 1, 1, 196417, 244801, 254017, 244801, 196417, 1, 1, 1572481, 1964161, 2056321, 2056321, 1964161, 1572481, 1, 1, 12582145, 15724801, 16498945, 16646401 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 39, 724, 9653, 109446, 1136455, 11185928, 106258185, 984268810,...}.

LINKS

Table of n, a(n) for n=0..40.

FORMULA

q=4;

f(n,m,q)=Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];

t(n,m,q)=1 - (f(n, k, q) + f(n, 2*n - k, q) - (f(n, 1, q) + f(n, 2*n - 1, q)))

EXAMPLE

{1},

{1, 1},

{1, 37, 1},

{1, 361, 361, 1},

{1, 3025, 3601, 3025, 1},

{1, 24481, 30241, 30241, 24481, 1},

{1, 196417, 244801, 254017, 244801, 196417, 1},

{1, 1572481, 1964161, 2056321, 2056321, 1964161, 1572481, 1},

{1, 12582145, 15724801, 16498945, 16646401, 16498945, 15724801, 12582145, 1},

{1, 100661761, 125821441, 132088321, 133562881, 133562881, 132088321, 125821441, 100661761, 1}

MATHEMATICA

f[n_, k_, q_] := Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];

t[n_, k_, q_] := 1 - (f[n, k, q] + f[n, 2*n - k, q] - (f[n, 1, q] + f[n, 2* n - 1, q]));

Table[Flatten[Table[Table[t[ n, k, q], {k, 1, 2*n, 2}], {n, 1, 10}]], {q, 2, 10}]

CROSSREFS

Sequence in context: A190301 A077575 A215258 * A272725 A057639 A190356

Adjacent sequences:  A176792 A176793 A176794 * A176796 A176797 A176798

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Apr 26 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 26 07:41 EDT 2021. Contains 347664 sequences. (Running on oeis4.)