login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A152238 A modulo two parity function as a triangle sequence:k=2; t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]]. 0
1, 1, 1, 1, 6, 1, 1, 15, 15, 1, 1, 12, 18, 12, 1, 1, 25, 30, 30, 25, 1, 1, 18, 75, 60, 75, 18, 1, 1, 35, 105, 175, 175, 105, 35, 1, 1, 24, 84, 168, 210, 168, 84, 24, 1, 1, 45, 108, 252, 378, 378, 252, 108, 45, 1, 1, 30, 225, 360, 630, 756, 630, 360, 225, 30, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: {1, 2, 8, 32, 44, 112, 248, 632, 764, 1568, 3248,...}. The k is added to give a quantum level to the resulting symmetrical functions.

LINKS

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

FORMULA

t(n,m)=Binomial[n,m]+p(n,m);

k=2;

p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]].

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 15, 15, 1},

{1, 12, 18, 12, 1},

{1, 25, 30, 30, 25, 1},

{1, 18, 75, 60, 75, 18, 1},

{1, 35, 105, 175, 175, 105, 35, 1},

{1, 24, 84, 168, 210, 168, 84, 24, 1},

{1, 45, 108, 252, 378, 378, 252, 108, 45, 1},

{1, 30, 225, 360, 630, 756, 630, 360, 225, 30, 1}

MATHEMATICA

Clear[p];

k=2;

p[n_, m_] = If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k*Binomial[n, m], 0]];

Table[Table[Binomial[n, m] + p[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A230073 A143210 A205133 * A086645 A168291 A154980

Adjacent sequences:  A152235 A152236 A152237 * A152239 A152240 A152241

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Nov 30 2008

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 5 19:19 EST 2016. Contains 278770 sequences.