Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A116157
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A116157 a(n)=a(n-1)+2a(n-2)-2a(n-3)+a(n-5). +0
1
1, 1, 3, 3, 7, 8, 17, 22, 43, 60, 110, 161, 283, 428, 732, 1132, 1901, 2984, 4950, 7848, 12912, 20609, 33721, 54065, 88137, 141737, 230490, 371411, 602982, 972961, 1577840, 2548288, 4129457, 6673335 (list; graph; listen)
OFFSET

0,3

COMMENT

A Fibonacci-Padovan sequence.

The summation over some naturally chosen planes in the pyramid composed of MacWilliams transform matrices yields this sequence, which is the convolution of the Fibonacci numbers and the (alternating) Padovan numbers. Namely, the formula F(n)= Sum[binomial[k,i],{i+k=n, i>0, k>0}]= Sum[Krawtchouk[{k,i},0],{i+k=n, i>0, k>0}], where Krawtchouk[{k,i},x] is the i-th Krawtchouk polynomial of order k has a natural generalization as G(n)= Sum[Krawtchouk[{k,i},j],{i+j+k=n, i>0,j>0, k>0}].

REFERENCES

N. Gogin and A. Myllari, The Fibonacci-Padovan sequence and MacWilliams transform matrices,Programming and Computing Software, Vol. 33, Issue 2 (March 2007), pp. 74 - 79.

FORMULA

G.f.: 1/((1-x-x^2)(1-x^2+x^3))

MATHEMATICA

a[0]=1; a[1]=1; a[2]=3; a[3]=3; a[4]=7; a[n_] :=a[n]=a[n-1]+2a[n-2]-2a[n-3]+a[n-5]; Table[a[n], {n, 0, 50}]

CROSSREFS

Cf. A000045, A000931.

Adjacent sequences: A116154 A116155 A116156 this_sequence A116158 A116159 A116160

Sequence in context: A086543 A110618 A108046 this_sequence A056357 A131036 A034411

KEYWORD

easy,nonn

AUTHOR

Nikita Gogin & Aleksandr Myllari (alemio(AT)utu.fi), Apr 15 2007

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified October 13 17:46 EDT 2008. Contains 145008 sequences.


AT&T Labs Research