|
|
A104882
|
|
Diagonal sums of number triangle A104881.
|
|
2
|
|
|
1, 1, 2, 3, 5, 8, 14, 24, 45, 85, 170, 351, 749, 1656, 3758, 8776, 21013, 51473, 129018, 329939, 860901, 2288528, 6192526, 17047248, 47693661, 135554549, 391099370, 1144867871, 3398656893, 10226072720, 31173964942, 96240485104, 300777706053
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/2)} ( Sum_{j=0..k} (n-2*k)^(k-j) ).
a(n) = Sum_{k=0..floor(n/2)} A104881(n-k, k).
|
|
MATHEMATICA
|
Table[Sum[If[j==k, 1, (n-2*k)^(k-j)], {k, 0, Floor[n/2]}, {j, 0, k}], {n, 0, 40}] (* G. C. Greubel, Jun 15 2021 *)
|
|
PROG
|
(Magma) [(&+[ (&+[ (n-2*k)^(k-j) : j in [0..k]]) : k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Jun 15 2021
(Sage) [sum(sum((n-2*k)^(k-j) for j in (0..k)) for k in (0..n//2)) for n in (0..40)] # G. C. Greubel, Jun 15 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|