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 A047372 Numbers that are congruent to {1, 2, 3, 5} mod 7. 1
 1, 2, 3, 5, 8, 9, 10, 12, 15, 16, 17, 19, 22, 23, 24, 26, 29, 30, 31, 33, 36, 37, 38, 40, 43, 44, 45, 47, 50, 51, 52, 54, 57, 58, 59, 61, 64, 65, 66, 68, 71, 72, 73, 75, 78, 79, 80, 82, 85, 86, 87, 89, 92, 93, 94, 96, 99, 100, 101, 103, 106, 107, 108, 110 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1). FORMULA From Bruno Berselli, Dec 01 2010: (Start) G.f.: x*(1+x+x^2+2*x^3+2*x^4) / ((1-x)^2*(1+x+x^2+x^3)). a(n) = (14*n+(3*i-1)*(-i)^n-(3*i+1)*i^n-(-1)^n-13)/8, i=sqrt(-1). (End) From Wesley Ivan Hurt, Jun 04 2016: (Start) a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. a(2k) = A047385(k), a(2k-1) = A047356(k). (End) E.g.f.: (8 + 3*sin(x) - cos(x) + (7*x - 6)*sinh(x) + 7*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, Jun 04 2016 MAPLE A047372:=n->(14*n+(3*I-1)*(-I)^n-(3*I+1)*I^n-(-1)^n-13)/8: seq(A047372(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016 MATHEMATICA Flatten[7Range[0, 12]+n/.n->{1, 2, 3, 5}] (* Harvey P. Dale, Dec. 13, 2010 *) PROG (MAGMA) [n : n in [0..150] | n mod 7 in [1, 2, 3, 5]]; // Wesley Ivan Hurt, Jun 04 2016 CROSSREFS Cf. A047356, A047385. Sequence in context: A002153 A047607 A113051 * A308469 A247547 A096974 Adjacent sequences:  A047369 A047370 A047371 * A047373 A047374 A047375 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)