Search: id:A002418
Results 1-1 of 1 results found.

%I A002418 M4617 N1970
%S A002418 0,1,9,35,95,210,406,714,1170,1815,2695,3861,5369,7280,9660,12580,
%T A002418 16116,20349,25365,31255,38115,46046,55154,65550,77350,90675,105651,
%U A002418 122409,141085,161820,184760,210056,237864,268345,301665,337995
%N A002418 4-dimensional figurate numbers: (5*n-1)*binomial(n+2,3)/4.
%C A002418 Partial sums of A002413.
%D A002418 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002418 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002418 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 195.
%H A002418 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A002418 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A002418 G.f.: x*(1+4*x)/(1-x)^5.
%F A002418 Starting (1, 9, 35, 95,...), = A128064 * A000332, (A000332 starting 1, 
               5, 15, 35, 70,...), such that a(n) = n*C((n+3),4)) - (n-1)*C((n+2),
               4)). E.g. a(5) = 210 = 5*C(8,4) - 4*C(7,4) = 5*70 - 4*35. - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2007
%F A002418 Unit digit, A010879(a(n)), is one of {0,1,9,5,6,4} [Eric Desbiaux] because 
               a(n) mod 5 = 0,1,4,0,0, periodic with period 5. [Proof: A002413(n) 
               mod 5 = 1,3,1,0,0 with period 5 and a(n) are the partial sums of 
               A002413.] - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2008
%p A002418 A002418:=-(1+4*z)/(z-1)**5; [S. Plouffe in his 1992 dissertation.]
%Y A002418 Cf. A093562 ((5, 1) Pascal, column m=4).
%Y A002418 Cf. A128064, A000332.
%Y A002418 Sequence in context: A071398 A005898 A034957 this_sequence A118414 A137628 
               A020297
%Y A002418 Adjacent sequences: A002415 A002416 A002417 this_sequence A002419 A002420 
               A002421
%K A002418 nonn
%O A002418 0,3
%A A002418 N. J. A. Sloane (njas(AT)research.att.com).

Search completed in 0.001 seconds