|
|
A051843
|
|
Partial sums of A002419.
|
|
10
|
|
|
0, 1, 11, 51, 161, 406, 882, 1722, 3102, 5247, 8437, 13013, 19383, 28028, 39508, 54468, 73644, 97869, 128079, 165319, 210749, 265650, 331430, 409630, 501930, 610155, 736281, 882441, 1050931, 1244216, 1464936, 1715912, 2000152, 2320857, 2681427
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
5-dimensional form of octagonal-based pyramidal numbers. - Derek I. Thomas (dithom02(AT)louisville.edu), Jun 30 2007
Also the number of 4-cycles in the (n+2)-triangular honeycomb bishop graph. - Eric W. Weisstein, Aug 10 2017
|
|
REFERENCES
|
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
H. J. Ryser, Combinatorial Mathematics, Carus Mathematical Monographs No. 14, John Wiley and Sons, 1963, pp. 1-8.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = C(n+3,4) * (6*n-1)/5
G.f.: x*(1+5*x)/(1-x)^6.
a(n) = n*(n+1)*(n+2)*(n+3)*(6n-1)/120. - Derek I. Thomas (dithom02(AT)louisville.edu), Jun 30 2007
|
|
MATHEMATICA
|
Join[{0}, Accumulate[LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 40, 110, 245}, 40]]] (* Harvey P. Dale, Nov 30 2014 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 11, 51, 161, 406}, 40] (* Harvey P. Dale, Nov 30 2014 *)
Table[(6 n - 1) Binomial[n + 3, 4]/5, {n, 0, 20}] (* Eric W. Weisstein, Aug 10 2017 *)
|
|
CROSSREFS
|
Cf. A093563 ((6, 1) Pascal, column m=5).
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(1) corrected by Gael Linder (linder.gael(AT)wanadoo.fr), Oct 31 2007
|
|
STATUS
|
approved
|
|
|
|