



1, 4, 7, 16, 25, 52, 79, 160, 241, 484, 727, 1456, 2185, 4372, 6559, 13120, 19681, 39364, 59047, 118096, 177145, 354292, 531439, 1062880, 1594321, 3188644, 4782967, 9565936, 14348905, 28697812, 43046719, 86093440, 129140161
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OFFSET

1,2


COMMENTS

Interleaving of A058481 and A100774 without initial term 0.
Apparently a(n) = A062318(n+2)1.
The terms beginning with a(2) are the row numbers in Pascalâ€™s Triangle where every 3rd element in those rows is divisible by 3 and none of the other elements in those rows are divisible by 3.  Thomas M. Green, Apr 03 2013


REFERENCES

Thomas M. Green, Prime Patterns in Pascal's Triangle, paper in review process, 2013.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,3).


FORMULA

a(n) = A038754(n+1)2. a(n) = A038754(n+2)2.
a(n) = 3*a(n2)+4 for n > 2; a(1) = 1, a(2) = 4.
a(n) = (5(1)^n)*3^(1/4*(2*n1+(1)^n))/22.
G.f.: x*(1+3*x)/((1x)*(13*x^2)).


EXAMPLE

For n = 3, a(3) = 7. The binomial coefficients of the 7th row of Pascal's Triangle are 1 7 21 35 35 21 7 1 and every 3rd element is a multiple of 3.  Thomas M. Green, Apr 03 2013


MATHEMATICA

Accumulate[Transpose[NestList[{Last[#], 3*First[#]}&, {1, 3}, 40]][[1]]] (* Harvey P. Dale, Feb 17 2012 *)


PROG

(MAGMA) T:=[ n le 2 select 2*n1 else 3*Self(n2): n in [1..33] ]; [ n eq 1 select T[1] else Self(n1)+T[n]: n in [1..#T]];
(PARI) a(n) = (2+n%2)*3^(n\2)2 \\ Charles R Greathouse IV, Jul 15 2011


CROSSREFS

Cf. A162436, A058481 (3^n2), A100774 (2*(3^n  1)), A062318, A038754, A038754.
Sequence in context: A095755 A245937 A259653 * A005513 A254323 A254143
Adjacent sequences: A164120 A164121 A164122 * A164124 A164125 A164126


KEYWORD

nonn,easy


AUTHOR

Klaus Brockhaus, Aug 10 2009


STATUS

approved



