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A164123 Partial sums of A162436. 4
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 (list; graph; refs; listen; history; text; internal format)
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 Pascal’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(n-2)+4 for n > 2; a(1) = 1, a(2) = 4.

a(n) = (5-(-1)^n)*3^(1/4*(2*n-1+(-1)^n))/2-2.

G.f.: x*(1+3*x)/((1-x)*(1-3*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*n-1 else 3*Self(n-2): n in [1..33] ]; [ n eq 1 select T[1] else Self(n-1)+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^n-2), 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

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Last modified March 28 19:06 EDT 2017. Contains 284246 sequences.