A221912 - OEIS

%I #31 Feb 12 2024 13:19:31

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,11,12,14,16,18,20,22,24,

%T 26,28,30,32,34,36,39,42,45,48,51,54,57,60,63,66,69,72,76,80,84,88,92,

%U 96,100,104,108,112,116,120,125,130,135,140,145,150,155

%N Partial sums of floor(n/12).

%C Apart from the initial zeros, the same as A008730.

%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,0,0,0,1,-2,1).

%F a(12n) = A051866(n).

%F a(12n+1) = A139267(n).

%F a(12n+2) = A094159(n).

%F a(12n+3) = A033579(n).

%F a(12n+4) = A049452(n).

%F a(12n+5) = A033581(n).

%F a(12n+6) = A049453(n).

%F a(12n+7) = A033580(n).

%F a(12n+8) = A195319(n).

%F a(12n+9) = A202804(n).

%F a(12n+10) = A211014(n).

%F a(12n+11) = A049598(n).

%F G.f.: x^12/((1-x)^2*(1-x^12)).

%F a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=0, a(11)=0, a(12)=1, a(13)=2, a(n)=2*a(n-1)- a(n-2)+ a(n-12)- 2*a(n-13)+ a(n-14). - _Harvey P. Dale_, Mar 23 2015

%e ..0....0....0....0....0....0....0....0....0....0....0....0

%e ..1....2....3....4....5....6....7....8....9...10...11...12

%e .14...16...18...20...22...24...26...28...30...32...34...36

%e .39...42...45...48...51...54...57...60...63...66...69...72

%e .76...80...84...88...92...96..100..104..108..112..116..120

%e 125..130..135..140..145..150..155..160..165..170..175..180

%e 186..192..198..204..210..216..222..228..234..240..246..252

%e 259..266..273..280..287..294..301..308..315..322..329..336

%e 344..352..360..368..376..384..392..400..408..416..424..432

%e 441..450..459..468..477..486..495..504..513..522..531..540

%e ...

%t Accumulate[Floor[Range[0,70]/12]] (* or *) LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,0,1,-2,1},{0,0,0,0,0,0,0,0,0,0,0,0,1,2},70] (* _Harvey P. Dale_, Mar 23 2015 *)

%Y Cf. A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470, A131242, A218530.

%K nonn,tabf,easy

%O 0,14

%A _Philippe Deléham_, Mar 27 2013