|
| |
|
|
A122931
|
|
Row sums of triangular array A122930.
|
|
2
| |
|
|
1, 2, 7, 18, 50, 132, 351, 924, 2431, 6380, 16732, 43848, 114869, 300846, 787815, 2062830, 5401054, 14140940, 37022755, 96928920, 253766591, 664375032, 1739365272, 4553731728, 11921847625, 31211839802, 81713718151, 213929389674
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| Also sums of the natural numbers with A000045 entries per row: for example 1 2 3+4 5+6+7 8+9+10+11+12.
|
|
|
FORMULA
| a(n)=sum_{i=A000071(n+1)+1..A000071(n+2)} i. a(n)=A000045(n)*[A000071(n+1)+{A000045(n)+1}/2]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 07 2006
a(n) = Sum_{k=1..n} [A000045(k)^2*A000045(n-k+1)] - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Nov 08 2007
a(n)=(F(n+2)^2-F(n+1)^2-F(n+2)+F(n+1))/2 where F(n)=Fibonacci(n). [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 10 2011]
|
|
|
MAPLE
| A000045 := proc(n) if n <= 1 then RETURN(n) ; else RETURN( A000045(n-1)+A000045(n-2)) ; fi ; end: A000071 := proc(n) RETURN(A000045(n)-1) ; end: A122931 := proc(n) local a45 ; a45 := A000045(n) ; RETURN (a45*(A000071(n+1)+(a45+1)/2)) ; end: for n from 1 to 30 do printf("%d, ", A122931(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 07 2006
|
|
|
CROSSREFS
| Cf. A000027 A000045 A001654 A003714 A010049 A035514 A122930.
Sequence in context: A017925 A030236 A074141 * A094976 A006869 A099626
Adjacent sequences: A122928 A122929 A122930 * A122932 A122933 A122934
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Sep 20 2006
|
|
|
EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 07 2006
|
| |
|
|
